Irrationality is cognition without rationality. This includes any thought, writing, speaking or actions that a person does without adequate reasoning behind them. It is often associated with mental illness, as the ability to think in a rational manner is part of the definition of having a sound mind, and also observed in people who are placed in stressful situations where the ability to rationalise actions is severely diminished. It's difficult to define any further because of the different subjective values of what counts as "rational" thinking.